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Calibration and Evaluation of Anisotropic Stress Functions Hill-48 and Karafillis-Boyce

In the present study, anisotropic elasto-plastic constitutive formulations for sheet metals based on associated or non-associated flow rule and four parametric anisotropic stress functions Hill-48 or Karafillis-Boyce are considered. By the standard approach, in non-associated formulations, anisotropy parameters of Hill-48 and Karafillis- Boyce yield function/plastic potential are calculated using experimental yield stresses/Lankford coefficients obtained in uniaxial tensile tests of sheet specimens with alignment 0°, 45° and 90° to the rolling direction. In addition, the equibiaxial yield stress is utilized in the calibration procedure for the yield function. In this way, under non-associated flow rule, all together seven experimental data are utilized in the model calibration. In the present study, application of genetic algorithms as optimization technique in calculating anisotropy parameters of Hill-48 and Karafillis-Boyce stress functions is considered. The analysed approach enables inclusion of greater number of experimental data as well as specific constraints in the model calibration. For the selected sheet materials, in the considered calibration procedure, experimental data related to the uniaxial tensile tests of seven sheet specimens with different alignment to the rolling direction are utilized. Furthermore, for the plastic potential function theoretical constraint related to the shear loading condition is included. For the obtained functions, contour shapes and predictions of the directional dependences of uniaxial tensile data are considered. The developed formulations are tested in predicting cylindrical cup deep drawing process.

anisotropic stress functions, calibration, genetic algorithm, sheet metals

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